Time taken to travel a certain distance of $x$ km at speed of $40 ext{ km/h}$ is 2 hours more than the time taken to travel $(x+20)$ km at speed of $60 ext{ km/h}$. Find the time taken to travel $(x+40)$ km at the speed of $40 ext{ km/h}$?

Question

Time taken to travel a certain distance of $x$ km at speed of $40 	ext{ km/h}$ is 2 hours more than the time taken to travel $(x+20)$ km at speed of $60 	ext{ km/h}$. Find the time taken to travel $(x+40)$ km at the speed of $40 	ext{ km/h}$?

Accepted Answer

**Solution:**

1. Let the distance be $x$ km.

2. Time taken to travel $x$ km at $40 	ext{ km/h}$ is $\frac{x}{40}$ hours.

3. Time taken to travel $(x+20)$ km at $60 	ext{ km/h}$ is $\frac{x+20}{60}$ hours.

4. According to the question, the time difference is 2 hours:
   $$\frac{x}{40} - \frac{x+20}{60} = 2$$

5. Find a common denominator for the left side: 120.

$$\frac{3x}{120} - \frac{2(x+20)}{120} = 2$$

6. Simplify numerator:
   $$3x - 2x - 40 = 240$$

$$x - 40 = 240$$

7. Solve for $x$:
   $$x = 280 	ext{ km}$$

8. Required time to travel $(x+40)$ km at $40 	ext{ km/h}$:
   $$\frac{280 + 40}{40} = \frac{320}{40} = 8 	ext{ hours}$$

**Answer:** 8 hours

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